Investigating the dynamics of the OPGG (Fig. REF  and Fig. SREF  in the Supplementary Materials), in the absence of both punishment and any reputational element, we reproduce the rock-paper-scissor dynamics between the three unconditional strategies as in [1]} and [2]}. When aggregated over time, this results in agents cooperating or defecting about 20% of the time each, while operating as loners about half of the time. Introducing the full set of punishing strategies as in [3]} we successfully reproduce their main result: the proportion of defectors and cooperators further diminishes with respect to the baseline, whilst the proportion of agents acting as loners increases. Having successfully replicated the key results of the extant literature, we investigate two models benchmarked respectively against the traditional OPGG and the OPGG with the full spectrum of punishment. In the first manipulation, we introduce a reputational system to the OPGG, while in the second we add it to the OPGG with punishment. In both cases we report results averaged over the second half of 100 simulations each comprising 200000 time steps.
<FIGURE>